How to make large, void free dust clusters in dusty plasma under microgravity
aa r X i v : . [ phy s i c s . p l a s m - ph ] A ug How to make large, void-free dust clusters in dustyplasma under microgravity.
V Land and W J Goedheer Center for Astrophysics, Space Physics, and Engineering Research, BaylorUniversity, Waco, TX, USA 76798-7316 victor [email protected] Abstract.
Collections of micrometer sized solid particles immersed in plamsa areused to mimic many systems from solid state and fluid physics, due to their strongelectrostatic interaction, their large inertia, and the fact that they are large enoughto be visualized with ordinary optics. On Earth, gravity restricts the so called dustyplasma systems to thin, two-dimensional layers, unless special experimental geometriesare used, involving heated or cooled electrons, and/or the use of dielectric materials.In micro-gravity experiments, the formation of a dust-free void breaks the isotropyof three-dimensional dusty plasma systems. In order to do real three-dimensionalexperiments, this void has somehow to be closed. In this paper, we use a fully self-consistent fluid model to study the closure of a void in a micro-gravity experiment, bylowering the driving potential. The analysis goes beyond the simple description of the”virtual void”, which describes the formation of a void without taking the dust intoaccount. We show that self-organization plays an important role in void formationand void closure, which also allows a reversed scheme, where a discharge is run at lowdriving potentials and small batches of dust are added. No hysteresis is found thisway. Finally, we compare our results to recent experiments and find good agreement,but only when we do not take charge-exchange collisions into account.PACS numbers: 52.27.Lw, 52.65.-y ow to make large, void-free dust clusters in dusty plasma under microgravity.
1. Introduction: Dusty plasma as a model system
The difference between dusty plasma and ordinary plasma is the presence of small solidparticles that collect electrons and ions from the surrounding plasma. This means thatthe dust particles charge up, and many forces start acting on them. The electrostaticinteraction between the shielded dust particles determines the internal structure ofthe dust clouds. The coupling between the particles depends on the ratio of theirmutual Coulomb interaction potential and their kinetic energy, which is usually referredto as the ”coupling parameter”, Γ = Q d exp( − ∆ /λ d ) / ∆ k b T d . Q d is the dust charge,∆ = (3 / πn d ) / , the inter-particle distance, and T d the dust kinetic temperature. It isworthwhile to mention that the latter is very hard to determine, but different methodsare used, see for instance [1].When Γ ≫ ≪ without taking the effect of the dust on the plasmaparameters into account. It is therefore valid only to describe experiments with a verylimited number of dust particles, such as in [11]. This was however not the case in theirexperiment.In this paper we perform numerical experiments to study the void closure in dustyplasma under microgravity, trying to bring more insight in the physics behind voidclosure in experiments, performed both in the recent past, as well as in current state-of-the-art machines [12]. The modelled discharge settings are exactly equal to those in [10], ow to make large, void-free dust clusters in dusty plasma under microgravity.
2. Numerical tool
A complete description of our model is given in [8], here we restrict ourselves to ashorter description. Our model solves both the plasma parameters, as well as the dustparameters in a coupled fashion. We start by briefly describing the solution for theplasma parameters.
Our fluid model solves the balance equation for a quantity A : ∂A∂t = −∇ · Γ A + S A , (1)assuming a drift-diffusion expression for the flux Γ A : Γ A = µ A A E − D A ∇ A, (2)which is then used in equation 1. Here S A represents the sources and sinks of quantity A , µ A the mobility, and D A the diffusion coefficient. We solve these equations for A = n e, + , for which we have the mobility as µ e, + = ∓ e/m e, + ν e, + with ν e, + the electron(ion) momentum transfer frequency. The diffusion coefficient is given by the Einsteinrelation D e, + = k b T e, + µ e, + . The source/sink terms in this case include electron impactexcitation, ionization, and recombination on the dust particles. For A = w e = n e ǫ , wehave µ w e = µ e . The sources and sinks are the same, but now also include the Ohmicheating term as a source, S Ohmic = J e · E . The ions are assumed to dissipate their heatinstantaneously, so that they are in equilibrium with the neutrals. Therefore, we do notsolve a similar equation for the ion energy density.In order to solve the above equation, we need to find the electric field from thePoisson equation: − ∇ V = − eǫ ( n e + n d Z d − n + ) , E = −∇ V, (3)with Z d the dust charge number. The ions are too heavy to follow the instantaneousfield E , but instead an effectieve field is found by solving d E eff /dt = ν + ( E − E eff ).All these equations are solved on sub-RF time-steps. However, the presence of Z d in the Poisson equation, as well the source terms for electron-ion recombination on thedust requires the solution of the dust density and charge. ow to make large, void-free dust clusters in dusty plasma under microgravity. The calculation of the dust charge is done by solving the current of electrons and ionsto the dust particles using Orbital Motion Limited theory [13], with the local plasmaparameters as input. In equilibrium, the currents balance, I + + I e = 0, and the surfacepotential V d is found. Assuming that the dust particles act as capacitors, the dust charge(number) is then found from Q d = eZ d = 4 πǫ r d V d . In case we include charge exchancecollisions, the ion current towards the dust particles is higher than the OML current.We calculate it with the analytic method derived in [14].The dust transport is solved by calculating the electrostatic force, F E , the ion dragforce, F ion , the thermophoretic force, F th , and the dust diffusion, which depends on theequation of state of the dust [15]. These forces are assumed to be in balance with theneutral drag F nd = m d ν m,d Γ d /n d , so that the dust flux can be written as: Γ d = n d F E m d ν m,d − D d ∇ n d + n d F th m d ν m,d + n d F ion m d ν m,d , (4)where ν m,d = (4 πr d / n gas v T ( m n /m d )), is the dust-neutral momentum transferfrequency, and E is the time averaged (over a RF period) electric field. The ion dragforce includes the effect of moderate non-linear scattering, anisotropic screening due toion drift, as well as the effect of cx-collisions [16, 17, 18]. The latter is similar to theeffect of these on the dust charging; a hot ion ”collides” with a cold atom, losing angularmomentum and energy, so that the probability to be captured by a nearby dust particleis increased. This increases the net ion current to the dust particles, increasing boththe ion drag force and reducing the negative charge on the dust. This in turn has thesecondary effect of reducing the ion drag force, since this force is ∝ Z d , as will be shownlater. The effect of these collisions on the ion drag force is always taken into account.We distinguish between cases with and without the effect on the charging.The dust transport is solved on longer time-steps. To maintain quasi-neutrality,the ion density is adapted, which causes a growing defect in the solution of the plasmadensities. When this defect becomes too large, the dust is frozen and the plasmaparameters are calculated again on sub-RF time-steps. The plasma and dust parametersare then completely coupled via the Poisson equation and the source-terms and wecompute towards the final equilibrium solution. Extending the dust flux equation to acomplete momentum equation, by including the total derivative of the density, to beable to look at the dynamic behavior of the dust transport, is something for future work,and is not included here.
3. The modelled discharge
The experiment we model is the Plasma Kristall Experiment, which was placed on boardof the International Space Station. This is a cylindrically symmetric RF discharge, runwith argon gas. We use the following discharge parameters: neutral pressure, P gas = 24Pa, background gas temperature, T gas = 293 K , RF-frequency ν RF = 13.56 MHz. We ow to make large, void-free dust clusters in dusty plasma under microgravity. V RF , peak-to-peakpotential V pp = 2 V RF ) is explained below. Figure 1.
The geometry of the experiment we model (the Plasma Kristall Experiment,PKE).
4. Determination of void size
To follow the analysis in [10], we first determine the virtual void size in the discharge.Dust particles added to a discharge will move to points where the total force acting onthem vanishes. When only a small number of particles is added to the discharge, sothat the plasma parameters are not influenced by the losses on the dust, these pointsform a contour where the outward ion drag force balances the inward electrostatic force,since the thermophoretic force is much smaller. This contour is called the virtual void.We determine the virtual void size, z v , as the distance between the central point andthe point where this contour crosses the axial symmetry line, in simulations where wedo not add any dust particles. So, we calculate the forces that would act on a dustparticle, if it would have been added to the discharge, and from that find the point onthe symmetry axis where this force vanishes, which is a rather straightforward method. The determination of the real void size, z r , when a large number of dust particles isadded is less straightforward. The contour where the ion drag and electrostatic forcebalance no longer coincides with the real inner boundary of the void, due to the pressureinside the dust cloud. In the experiment, an estimate for the dust density is made fromthe inter-particle distance. From this then, the inner boundary of the dust cloud canalso be determined. We determine the real void size as that point on the symmetry ow to make large, void-free dust clusters in dusty plasma under microgravity. n c = 10 m − . This choice is arbitrary, butcorresponds roughly to 10 % of the maximum density.Of course, it is rare that the density on one of the grid points in our simulationhas exactly this value. Therefore, we need to interpolate the dust density between gridpoints. We designate the real void size to be the distance between the point where theinterpolated line (or ‘fit’) then crosses this value and the center of the discharge, again,along the symmetry axis. The interpolation we use is not arbitrary, but based on theexponential scheme used to solve the dust flux. This exponential scheme is based onthe assumption of a constant drift-diffusion flux between successive grid points.In one direction (along the symmetry axis), this reads:Γ d = n d u d − D d ∂ z n d = C, (5)with u d the dust speed from the forces acting on the dust. Trying a solution of theform n d ( z ) = A + B exp( αz ), with 2 boundary conditions for n d ( z ), the lower value n d ( z ) = n l < n c , and the upper value n d ( z ) = n u > n c , where z = z + ∆, with ∆ thegrid-interval, we find the solution as, n d ( z ) = n l + n u − n l exp (cid:16) u d D d ∆ (cid:17) − (cid:18) exp (cid:18) u d D d ( z − z ) (cid:19) − (cid:19) , z ∈ ( z , z ) . (6)To find z r , we need to solve n d ( z r ) ≡ n c = n l + n u − n l exp (cid:16) u d D d ∆ (cid:17) − (cid:18) exp (cid:18) u d D d ( z r − z ) (cid:19) − (cid:19) , z r ∈ ( z , z ) . (7)This way, we find z r = z + D d u d ln (cid:20) n c − n l n u − n l (cid:18) exp (cid:18) u d D d ∆ (cid:19) − (cid:19)(cid:21) . (8)
5. Results: Virtual void sizes
We start with a dust free discharge, running at V RF ∼
30 V. We determine the virtualvoid size, and then reduce the potential in small steps. At different values of the drivingpotential we calculate the virtual void size. We do this set of calculations with andwithout cx-collisions (which is from now on to be understood as; with and without theeffect of cx-collisions on the dust charge). The results are shown in figure 2 on the left.First of all, we indeed see that the void decreases for decreasing driving potential,which coincides with the decrease in plasma density, as shown in figure 2 on the right.A decrease in ion density results in a decrease of the ion drag force, since the collectedand scattered ion flux is proportional to the ion density.Secondly, we see that the void sizes with collisions are simply shifted downwardswith respect to the solutions without collisions. This is not due to any changes inthe plasma because of additional plasma recombination, since in these virtual void ow to make large, void-free dust clusters in dusty plasma under microgravity.
10 15 20 25 300123456 V i r t u a l v o i d s i z e ( mm ) V RF (V) With CX collisions No collisions AB
10 15 20 25 30 35024681012 C e n t r a l p l as m a d e n s i t y ( m - ) V RF (V) Density, no dust
Figure 2. Left:
The obtained virtual void sizes with cx-collisions, indicated bythe black squares and line, labeled ’A’, and without cx collisions, indicated by thered triangles and line, labeled ’B’.
Right:
The central electron density without anydust present (because of quasi-neutrality, it equals the central ion density), for differentvalues of the driving potential. Clearly, the plasma density drops linearly for decreasingdriving potential. calculations, no dust is added to the simulation. However, the dust charge is evaluatedeverywhere, with the plasma parameters as input, even without dust particles present.With collisions, the calculated ion current towards dust particles increases, so that thedust charge becomes less negative. Since the ion drag force ∝ Z d , and the electrostaticforce ∝ Z d , the virtual void size decreases when the charge decreases when the collisionsare taken into account.Thirdly, we see that for larger driving potentials the two solutions approach eachother, whereas for lower driving potentials there is a large difference between the two.For increasing driving potential, the plasma density increases, so that the Debye lengthdecreases. This means that on average a fast ion approaching a dust particle collidesless times within a Debye length. Thus, the ion is unable to lose sufficient energy andangular momentum to reach the dust particle. The additional ion current towards thedust because of cx-collisions is therefore less, and the dust charge will be closer to thevalue without any cx-collisions.Finally, we see that the virtual void doesn’t decrease exactly proportional to theplasma density. For high potential, the decrease is linear, but for lower driving potential,approaching the point of vanishing virtual void, the decrease becomes much steeper. Thevirtual void size is determined by the ratio of the outward ion drag force over the inwardelectrostatic force, η = F ion /F E , since the virtual void is that point where this ratio is exactly one. Writing out the two forces (using the scattering part of the ion drag only,which is much larger than the collection part), this ratio becomes: η ( z ) = (cid:20) e Z d ( z ) µ + πǫ m + (cid:21) × n + ( z ) v s ( z ) ≈ · − n + ( z ) v s ( z ) , (9)where v s = q v T + + u is the total ion velocity, v T + = p T + /m + the ion thermal velocity ow to make large, void-free dust clusters in dusty plasma under microgravity. u + = µ + E the ion drift velocity. Assuming a constant dust charge, Z d ≈ , we seethat for typical plasma densities ( n + ≈ m − ) the total ion velocity at the virtualvoid edge ( η ≡
1) should be (2-3) × v T + , consistent with previous simulations [8].The virtual void size is thus determined by the density profile as well as by thedrift velocity of the ions. In terms of the drift velocity, there are two limits for equation9, the first when the ion drift is subthermal ( u ≪ v T + ), and second when the driftis suprathermal ( u ≫ v T + ). In the first limit η ∝ n + /v T + , so, η ∝ n + (since v T + isconstant). The latter limit gives η ∝ n + /u . One could argue that the decrease in n + , and the corresponding increase in the Debye length, results in an increase in u + ,because of an increase in charge separation and the corresponding electric field. Then,the change in the virtual void size curve could be due to this transition from subthermalion flow to suprathermal ion flow. Even though this might play a role, the basic shapeof the curve can be completely explained by a decrease in density only. E t a P l as m a d e n s i t y ( m - ) Z (mm)
28 V (A) 24 V 22 V 18 V 15 V 13 V 12 V (G)
ADG
10 12 14 16 18 20 22 24 26 28 30456789 Z V ( mm ) V RF (V) Figure 3. Left:
We approximate the axial density with an exponentially decayingdistribution. The central density at V RF = 28 V sets η < ∼
14 there. The densityvanishes at the upper electrode at z=15mm. For decreasing V RF the density profileflattens. Right:
The virtual void size, determined from the points where η = 1 forthe different driving potentials in the figure on the left. Even though the exact valuesare not right, the shape of the virtual void curve found by our simulations is wellrepresented. The effect of the changing density is illustrated in figure 3 with a simple qualitativemodel, for subthermal ion drift, so that η ∝ n . For illustrative purposes, we haveassumed that the density along the symmetry axis can be described by a bell-shapedcurve. The boundary values are the central value of the density on the left, given byfigure 2, and vanishing density at the upper electrode at z=15 mm. For decreasingdriving potential, the central density decreases and this leads to a more and more flatdensity profile. The central value for V RF = 28 V , ∼ m − , gives η ∼
14. whichfixes the right axis. The flatter the density profile, the larger the virtual void has toshift inwards in order to reach the point η = 1. Plotting the virtual void size found this ow to make large, void-free dust clusters in dusty plasma under microgravity. V RF gives the qualitative picture on the right. We see that, even thoughthe exact numbers are not correct, the shape of the virtual void as found in figure 2 iswell reproduced. This shows that the inward shift of the virtual void with decreasingpotential is due to the decrease in ion density inside the virtual void.Now that we have an understanding of the behavior of the virtual void in a plasmawithout any dust particles added, so that we understand where a very small number ofdust particles would reside at different driving potentials, we continue by investigatingthe behavior of the real void edge, when hundreds of thousands of dust particles areadded and the plasma parameters change dramatically.
6. Results: Real void sizes
A typical solution for the dusty plasma with void is shown in figure 4. The void is clearlyseen, and the plasma is confined inside the void. The dust density is of the order 10 m − , and the electron density is of the order of 10 m − . The electron temperature T e is roughly 3 ∼ Figure 4.
The initial dust density in 10 m − on the left, and the electron densityon the right in 10 m − for a dust cloud containing 500.000 particles. The void isclearly seen, and also that the plasma is confined within the volume of the void. The real void sizes for different simulations are shown in figure 5. Starting with thesimulations with 5 · particles with (red line and symbols, labeled ’A’) and without(black line and symbols, labeled ’B’) cx-collisions, we see that they show the samebehavior as the virtual void solutions. However, the potentials at which the real voidsclose are much higher. This is due to the additional losses of plasma on the dust particlesand consequently the larger decrease in the ion density and ion drag force. We also seethat the solutions are further apart in these results with dust particles. Not only isthe charge on the dust particles reduced by the enhanced ion current, but by the samemechanism the recombination rate of plasma on the dust is even more increased, so thatthe solutions are much further apart, the void without collisions closing at V RF = 18 . V ,the solution with collisions at V RF = 25 V . ow to make large, void-free dust clusters in dusty plasma under microgravity.
18 20 22 24 26 28 30 32 340123456 R ea l v o i d s i z es ( mm ) V RF (V) AB C
Figure 5.
The real void sizes for different simulations. The black squares indicatereal void sizes for a total of 5 · dust particles added to the discharge, withouttaking cx-collisions into account. The red diamonds indicate the same number of dustparticles, but now with cx-collisions. The blue stars are experimental results from [10].The blue star with z r = 0 is not plotted in their results but mentioned in the text.The green squares is a run with 1 . · particles, with cx-collisions. The error barsindicate a standard error due to the exponential fit to the density. When the voltage is decreased below the value needed to sustain the discharge,the ionization is no longer sufficient to compensate the losses at the walls and on thedust. Then, the electron density goes to zero, and the remaining dust-ion plasma willdecay by recombination and slow ambipolar diffusion, eventually leading to shut-downof the discharge. The final point without collisions is very close to this potential, sothat we could not go much lower in driving potential while keeping a stable void-freedusty plasma. The solution with collisions, however, was much more stable and didallow a significant range of driving potentials, while at the same time maintaining avoid-free dusty plasma, as indicated by the points all having z r = 0. The same holdsfor the solution with 130.000 particles added (green line and symbols, labeled ’C’). Thismeans that the same solution can also be found by starting with a dust-free dischargeat low potential and by adding small numbers of dust, while increasing the potential.This scheme might be less prone to shut-down of the plasma and might provide a moresuitable route to obtaining void-free dust crystals.It is interesting to note that the void size for higher driving potentials becomeslarger than in the case with 500.000 particles, without collisions. When we look at theelectron and ion densities inside the void, shown in figure 6, we see the effect of thedust on the plasma parameters; the plasma density is increased inside the void, as longas the driving potential is high enough. This was also discussed in [9]. The additionallosses are compensated by additional ionization, for which electron heating due to theincreased resistivity provides the necessary energy. The void shows self-organization,through which it maintains itself, despite the plasma-losses. However, once the drivingpotential becomes too low, the system can no longer provide enough energy to maintain ow to make large, void-free dust clusters in dusty plasma under microgravity.
12 14 16 18 20 22 24 26 28 30 32 34024681012141618202224 C e n t r a l d e n s i t y ( m - ) V RF (V) n e , 130k, col n + , 130k, col n + , 500k, col n e , 500k, col n + , 500k, no col n e , 500k, no col n + , no dust n e , no dust AB CD A BCD
Figure 6.
The central density for the different runs. The squares represent the electrondensity, the triangles the ion density. The colors represent different sets of runs, thegreen, labeled ’A’ has 130.000 particles, with cx-collisions, the red, labeled ’B’ has500.000 particles, with cx-collisions, the black has 500.000 particles, without collisions.The densities without dust are included for comparison, shown by the straight blacklines with small symbols, labeled ’D’.
A charge-separation arises once the void closes, especially in the case of cx-collisions,where the plasma absorption is very large. Effectively, the resulting dusty plasmaconsists mainly of negatively charged dust particles and free ions. After void closure,the net space charge will be zero, but the moments before the closure of the void, thereis a large positive charge inside the void, resulting in an electric field much larger thanthe ambipolar field, so that ion drifts are significant.Returning to figure 5, we have added some of the experimental points presentedin [10]. In that experiment several millions of particles were present in the discharge,but from the figures it was clear that not all the particles were involved in the closingof the void, but only a small subgroup of the particles in the cloud, close to the centerof the discharge. In our simulations we find a good agreement of our simulations with500.000 particles with the experimental points without cx-collisions, especially at thelower driving potentials, near void-closure. The point of void-closure reported was 18.3Volts, even though this point is not depicted in a graph. It is striking how well this valuecoincides with the point we find in our simulations, i.e. 18.2 Volts. It was also reportedthat the discharge was very near the point of shut-down, similar to our findings.The simulations including cx-collisions, which have been shown to be veryimportant in typical dusty plasmas as the one considered here, give a much higher valuefor the driving potential at void closure. We do not propose that cx-collisions should be ow to make large, void-free dust clusters in dusty plasma under microgravity.
7. Dust clouds obtained after void-closure
Radial (mm) A x i a l ( mm ) Radial (mm) A x i a l ( mm ) Figure 7. Left:
The final dusty density distribution (10 − m − ) for 500.000 dustparitcles, without cx-collisions, showing how there still is a strong minimum of thedust density in the center, where the void used to be. Right:
The same as on the left,but now with taking cx-collisions into account. The anisotropy is smaller, but is stillthere.
First, we show the final dust clouds in the dusty plasma discharges with 500.000added dust particles. Figure 7 shows the solution without collisions on the left, thesolution with collisions on the right. It is clear that, even though the void is closed ow to make large, void-free dust clusters in dusty plasma under microgravity.
20 25 30 35-0.25-0.20-0.15-0.10-0.050.000.050.100.150.200.25 Fo r ce ( - N ) Z (mm)
Total Force (A) F TH (B) F E +F ION (C)
AB C 20 25 30 35-0.20-0.15-0.10-0.050.000.050.100.150.20 Fo r ce ( - N ) Z(mm)
Total force (A) F TH (B) F E +F ION (C)
A B C
Figure 8. Left:
The axial forces in the dust cloud for 500.000 added particles, withoutcx-collisions. There is a residual outward ion drag force, which acts against the internaldust pressure, and causes the dip in dust density.
Right:
The same as on the left, butnow with taking cx-collisions into account. The electrostatic force and ion drag forcealmost completely vanish. Due to the increased plasma depletion, the background gasis heated more, however, causing an increased thermophoretic force, which enhancesthe anisotropy.
When we introduce less particles, the effect of the background gas heating mustbe less, since the plasma depletion on the dust is less. Indeed, the final dust cloud for130.000 particles, with cx-collisions, shown in figure 9 on the left is homogeneous, verysuitable for the experiments mentioned before. On the right, the same figure shows theforces throughout the dust cloud. The ion drag force and electrostatic force act void-closing, and have almost vanished, due to the very low space charge. The dusty plasmain the cloud acts much like an electronegative discharge that way. The thermophoreticforce is smaller and almost equal in magnitude, but opposite in sign to these forces. Thenet effect is a dust cloud where only the dust pressure determines the force, causing avery homogeneous dust cloud. ow to make large, void-free dust clusters in dusty plasma under microgravity. Radial (mm) A x i a l ( mm )
20 24 28 32 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 Fo r ce ( - N ) Axial (mm)
Net force (A) F TH (B) F E +F ION (C)
A B C
Figure 9. Left:
The final dust cloud in the discharge with 130.000 particles addedand with the effect of cx-collisions on the charging. A large, 3D, homogeneous, dust-free crystal has formed.
Right:
The forces acting on the dust inside the cloud. Thesum of the electrostatic and ion drag force has changed sign, only showing one pointwhere it vanishes, much like an electronegative discharge. The thermophoretic force issmall, but still comparable to the other forces, creating a large volume where the dusttransport is determined by the internal pressure only.
8. Conlcusions
Using a fully self-consistent fluid model for dusty plasmas, we have studied the behaviorof dusty plasma under micro-gravity conditions, while closing the void by lowering thedriving potential. The simulations without dust show how the virtual void closes withdecreasing potential. This is due to the decrease in plasma density, which causes adecrease of the outward ion drag. For decreasing density, and increasing Debye length,the ion drift velocity can increase, but as long as the drift inside the void is subthermal(as it usually is), the density profile determines the shift of the virtual void inwards. Theflattening of this profile along the symmetry axis explains why for high driving potentialthis shift is gradual, but becomes much faster for lower driving potentials. The effectof charge-exchange collisions on the virtual void is a decrease of this void-size for allpotentials, since the calculated charge on the dust becomes less.The real void-size, when many dust particles are added, shows a similar behavior,but now the plasma density behaves completely different, due to the additional depletionof plasma on the dust. The corresponding self-organization of the dusty plasma systemresults in additional ions that provide the outward force to maintain the void. Oncethe driving potential becomes too low to maintain this self-organization, the void closesrapidly due to a sudden loss of plasma. This is even more pronounced with charge-exchange collisions, due to the additional plasma losses. When the void closes, essentiallya negative dust particle-positive ion plasma is formed, which can be seen by the large ow to make large, void-free dust clusters in dusty plasma under microgravity. not taking the charge-exchange collisions intoaccount when calculating the dust charge, especially close to the point of void-closure.This might be due to the fact that at that point, the dust density becomes so highthat the inter-particle distance becomes comparable to the Debye length. This mightreduce the effect of charge-exchange collisions, so that the results without these arecloser to the experimental points. Also, an OML-based description of the dust chargingis no longer valid, since this theory is derived for isolated particles. A more thoroughdescription would be needed to quantitatively describe the points near void-closure,which apparently are less influenced by cx-collisions than previously expected.The final dust distributions are found to be homogeneous only when charge-exchange collisions are taken into account and when not too many dust particlesare added to the discharge. The electronegative character of the dust cloud playsan important role in minimizing the forces inside the dust cloud, together withthe thermophoretic force, due to the enhanced background gas temperature throughthe additional plasma recombination. This, in a sense, is another example of self-organization in dusty plasma. These dust crystals are so stable, that they allow thedusty plasma to be run at a rather large range of potentials below the point of voidclosure. This means that these crystals can also be formed by following the oppositescheme, namely by running a plasma at low potential and by adding small batches ofdust, while increasing the potential. This way, the discharge is less likely to die out,which might provide a more stable way of forming void-free dust crystals, which areneeded for the study of many phenomena on a scale directly visible to the naked eye. ow to make large, void-free dust clusters in dusty plasma under microgravity. References [1] J. D. Williams, E. Thomas, Jr., Phys. Plasmas 14, 063702 (2007)[2] H. C. Lee, B. Rosenstein, Phys. Rev. E , 7805 (1997)[3] S. Nunomura, J. Goree, S. Hu, X. Wang, A. Bhattacharjee, and K. Avinash, Phys. Rev. Lett. ,035001 (2002)[4] G. E. Morfill, M. Rubin-Zuzic, H. Rothermel, A. V. Ivlev, B. A. Klumov, H. M. Thomas, U.Konopka, V. Steinberg, Phys. Rev. Lett. , 175004 (2004)[5] D. Block et al Plasma Phys. Control. Fusion , B109-B116 (2007)[6] H. Rothermel, T. Hagl, G. E. Morfill, M. H. 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